Interplay between teleportation fidelity and basis-independent coherence in maximally sliced states under decoherence

Anushree Pandey; Sovik Roy

REVIEW 3 major objections 3 minor 38 references

Interplay between teleportation fidelity and basis-independent coherence in maximally sliced states under decoherence

T0 review · 3 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read For noisy three-qubit maximally sliced states, this paper derives closed-form relations between teleportation fidelity and basis-independent coherence, showing that phase damping preserves a universal coherence-fidelity curve while amplitud

desk verdict AD coherence–fidelity relation built on a wrong reduced density matrix; PD and ideal sections are correct but reparametrize known results. read the letter →

arxiv 2608.03865 v1 pith:HET6AQQ5 submitted 2026-08-04 quant-ph

Anushree Pandey , Sovik Roy This is my paper · ORCID

classification quant-ph

keywords quantumteleportationmaximallyslicedstatebasis-independentcoherenceamplitudedampingphasefidelitythree-tangledecoherence

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper addresses a gap: for the three-qubit maximally sliced (MS) state, no one had written down an explicit analytic relationship between teleportation fidelity, the operational measure, and basis-independent coherence, the resource measure, after noise. Using Kraus operators for amplitude damping (AD) and phase damping (PD), it derives closed-form expressions for both quantities on the reduced two-qubit channel and for the three-tangle parametrization. The main insight is that under phase damping the dephasing parameter cancels completely, leaving a single universal coherence-versus-fidelity curve; under amplitude damping the coherence retains explicit dependence on the damping probability, so fidelity alone does not determine coherence. The paper argues this distinction reflects the physical difference between pure dephasing, which only erases coherences, and energy dissipation, which also repopulates levels. A sympathetic reader would care because it gives a resource-based way to predict when a noisy MS state can still beat the classical teleportation threshold.

What carries the argument

Maximally Sliced state |MS(θ)⟩=(|000⟩+cosθ|110⟩+sinθ|111⟩)/√2, a one-parameter GHZ-class state; reduced channel ρ_AB=Tr_C ρ_ABC; maximal singlet fraction f_max and the standard conversion F_Tel=(2f_max+1)/3; the basis-independent coherence measure C_BI(ρ)=√{[S((ρ+I/d)/2)−S(ρ)+log₂d]/2}; single-qubit amplitude- and phase-damping Kraus operators; and the CKW three-tangle τ=sin²θ used to rewrite the state parameter. The machinery works by expressing both operational performance and resource content in terms of the same noise-dependent reduced density matrix, then eliminating the state parameter.

What would settle it

Apply the single-qubit AD Kraus operators (18) independently to each qubit of |MS(θ)⟩, trace out qubit C, and compare the resulting 4×4 matrix with Eq. (23). A direct computation gives diagonal entries (1+p²)/2 for |00⟩ and (1−p)²/2 for |11⟩, with off-diagonal (1−p)cosθ/2; at p=1 the reduced state is |00⟩⟨00|, not the paper's balanced mixture. This comparison settles whether Eq. (23), and therefore the claimed AD coherence-fidelity relation, is correct.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is the pair of explicit coherence-fidelity relations for three-qubit MS states. After tracing out the third qubit, the shared channel has maximal singlet fraction f_max, and the teleportation fidelity is F_Tel=(2f_max+1)/3. Under amplitude damping (probability p) this gives F_AD=[2+(1-p)(cosθ-p)]/3, with a quantum-advantage threshold p_c=cosθ; under phase damping (probability λ) it gives F_PD=[2+cosθ(1-λ)^2]/3, which stays above 2/3 for all nontrivial MS states until λ=1. Evaluating basis-independent coherence on the same reduced states and substituting the fidelity expressions produces Eq. (30) for AD and Eq. (38) for PD. The claimed result is

Load-bearing premise

The whole amplitude-damping analysis rests on the reduced density matrix in Eq. (23) having equal |00⟩ and |11⟩ diagonal entries; if direct application of the damping operators gives different entries, the AD fidelity and coherence formulas do not stand.

Editorial extensions

If this is right

For any MS state with cosθ>0, phase damping cannot kill the teleportation advantage before complete dephasing; the fidelity stays above the classical bound 2/3 for all λ<1.
Under amplitude damping, the critical value p_c=cosθ gives a directly testable prediction: the same resource that tolerates strong dephasing fails at a state-dependent energy-loss rate.
Because the phase-damping coherence-fidelity curve is universal, measuring either quantity fixes the other without knowing λ; this could serve as a noise-robust calibration of teleportation channels.
Expressing fidelities through τ=sin²θ connects a genuine tripartite entanglement measure to a bipartite teleportation task, showing that the initial three-party resource, not just the reduced state, sets the noise threshold.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same 'common multiplicative factor' mechanism that makes PD universal should generalize to any noise that multiplies all off-diagonal reduced-state coherences by one factor while leaving populations unchanged; unitary or symmetric dephasing models are natural candidates.
A direct consequence the authors leave implicit is that the ratio F_PD−2/3 over cosθ is (1−λ)^2, so a single experiment measuring fidelity at two dephasing strengths could infer λ and then predict the full coherence curve.
Applying the same derivation to generalized amplitude damping or depolarizing channels would test whether the breakdown of the one-to-one coherence-fidelity relation is specific to population-changing noise or generic.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know two things about this paper before spending time on it. First, the central claimed new result—an analytical relation between basis-independent coherence and teleportation fidelity for the MS state under amplitude damping—does not hold because the reduced density matrix in Eq. (23) is wrong. Second, the phase-damping and ideal-state sections are correct, but they are reparametrizations of known quantities rather than new results.

The issue in the AD section is concrete. Since the AD channel is trace-preserving on qubit C, you can trace out C first and apply the channel to A and B. Doing that gives diagonal entries (1+p^2)/2 for |00> and (1-p)^2/2 for |11>, not the paper's (1-p+p^2)/2 for both. The sum is the same, so the teleportation fidelity in Eq. (28) survives, but the eigenvalues are different: the correct |00>/|11| block has eigenvalues [1-p+p^2 ± sqrt(p^2 + (1-p)^2 cos^2θ)]/2, while Eq. (23) gives [1-p+p^2 ± (1-p)cosθ]/2. Everything built on these eigenvalues—Eqs. (24), (25), and the coherence–fidelity relation Eq. (30)—is therefore invalid. A simple check: at p=1 the true state is |00><00|, not the paper's 1/2(|00><00|+|11><11|).

What the paper does well: the PD section is clean. The reduced state under phase damping has the same form as the ideal state up to a factor (1-λ)^2 on the off-diagonal, so the coherence–fidelity relation matches the ideal one. That part is correct, though it is a reparametrization of a known expression: both C_BI and F_PD depend on cosθ(1-λ)^2. Similarly, the ideal-state relation is a monotone function of cosθ and not new. The three-tangle parametrization is a trivial substitution.

The paper is self-contained and honest; no fitted parameters, no invented entities. The heavy self-citation is to background work, not to the derivation, so that is not a real issue.

My take: this should not be accepted as is. The main result is wrong. If the AD calculation is fixed, the paper would still be modest—an explicit AD coherence–fidelity relation for this state family—but at least it would be correct. I would send it to a referee who can check the algebra, but I would expect a rejection unless the calculation is corrected and the novelty is stated more carefully.

For your purposes: not worth citing, but a useful example of how a small error in a reduced density matrix can invalidate a whole section. I might bring it to a reading group as a cautionary tale.

Referee Report

3 major / 3 minor

Summary. The paper studies the three-qubit maximally sliced (MS) state |MS(θ)> = (|000> + cosθ|110> + sinθ|111>)/√2 as a resource for quantum teleportation. Tracing out one qubit and using the maximal singlet fraction, the authors derive teleportation fidelities for the ideal state and under amplitude damping (AD) and phase damping (PD) channels, with Kraus-operator noise applied to all three qubits. They also evaluate the Radhakrishnan basis-independent coherence of the reduced two-qubit state and claim explicit analytical coherence–fidelity relations (Eqs. 17, 30, 38), expressed further in terms of the CKW three-tangle. The ideal-state and three-tangle sections are elementary and appear correct, and the paper is self-contained with no fitted parameters. However, the central AD and PD coherence calculations rest on incorrect reduced density matrices, invalidating the main claimed new results.

Significance. If correct, the closed-form coherence–fidelity relations for MS states under amplitude and phase damping would be a useful contribution, connecting a basis-independent resource measure to teleportation performance and providing a concrete comparison of the two noise channels. The paper is written in a self-contained manner using standard definitions (Kraus operators, Horodecki fidelity, Radhakrishnan coherence, CKW tangle) with no free parameters. The ideal-state treatment and the three-tangle parametrization are sound. However, the AD and PD sections contain load-bearing algebraic errors that propagate into the central claims; these are not mere presentation issues.

major comments (3)

[§4, Eq. (23)] The amplitude-damped reduced density matrix is incorrect. Direct application of the AD Kraus operators (18) to ρ_AB of Eq. (6) — legitimate because tracing out qubit C commutes with a trace-preserving channel on C — gives the |00> diagonal element (1+p²)/2 and the |11> diagonal element (1−p)²/2, not (1−p+p²)/2 for both. The off-diagonal element is (1−p)cosθ/2 as stated. At p=1 the correct reduced state is |00><00|, whereas Eq. (23) gives ½(|00><00| + |11><11|). Consequently the eigenvalues quoted in Eq. (25) are wrong and the coherence expressions Eqs. (24) and (30) are invalid. The teleportation fidelity Eq. (28) happens to survive because the sum of the |00> and |11> populations is unchanged, but the claimed AD coherence–fidelity relation Eq. (30) is unsupported.
[§4, Eqs. (24)–(25)] Even taking Eq. (23) at face value, the eigenvalue list in Eq. (25) is internally inconsistent. The eigenvalues of the matrix in Eq. (23) are (1−p+p² ± (1−p)cosθ)/2 and p(1−p)/2 (twice), whereas Eq. (25) gives λ1,2 = (1−p+p² ± (1−p)cosθ)/4. Thus Eq. (24) does not compute the basis-independent coherence of the state written in Eq. (23). The μ3 entry is also off by a factor of 2 from the eigenvalues of (ρ+I/4)/2. This reinforces that all AD coherence results in this section are unreliable.
[§5, Eq. (33)] The phase-damping reduced density matrix also appears to have an incorrect off-diagonal factor. With the Kraus operators of Eq. (31), K_PD0 = diag(1,√(1−λ)) and K_PD1 = diag(0,√λ), a single qubit coherence element ρ01 decays by √(1−λ), not by (1−λ). Applying the channel to qubits A and B therefore gives the off-diagonal element of ϱ_PD_AB as (1−λ)cosθ/2, not (1−λ)²cosθ/2. Consequently Eq. (37) should read F_PD = [2 + (1−λ)cosθ]/3, and Eq. (38) is derived from the wrong input. A direct check at λ=1/2, θ=0 gives <φ+|ϱ_PD_AB|φ+> = 3/4, whereas Eq. (35) gives 5/8. The qualitative ‘preserved one-to-one correspondence’ may survive, but the quantitative PD formulas are wrong.

minor comments (3)

[§2.3, Eq. (9)] The displayed formula for basis-independent coherence is ambiguous: the placement of the division by 2 is unclear. The algebraic expressions that follow (e.g., Eq. (16)) do not transparently follow from the displayed definition; a clean derivation should be provided.
[Table 1] Table 1 refers to “Eq. (41)” for the PD coherence–fidelity relation and “Eqs. (48)–(50)” for the three-tangle representation, but these equation numbers do not exist in the text. The corresponding equations are (38) and (45)–(47).
[References] References [17] and [26] appear to be the same arXiv preprint repeated with different numbering. Additionally, Figures 1–3 are described in the text but not displayed in the manuscript text provided; please ensure they are included in the final version.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; derivations are self-contained given standard definitions, though the AD channel results contain an independent arithmetic error.

full rationale

The paper's derivation chain is self-contained. The MS state is defined explicitly (Eq. 1), and the reduced density matrices for the ideal, amplitude-damped, and phase-damped cases are computed directly from the Kraus operators and partial trace. The teleportation fidelity follows from the Horodecki formula (Eq. 8) applied to the maximal singlet fraction, and the basis-independent coherence follows from the Radhakrishnan et al. definition (Eq. 9). No parameters are fitted to data, and no result is imported from the target conclusion. The 'coherence–fidelity relations' (Eqs. 17, 30, 38) are algebraic reparametrizations of the fact that both quantities are functions of the same underlying density matrix; this is a coordinate change, not a circular definition. The heavy self-citation in the references is contextual (prior work on related states and coherence measures) and is not used as a load-bearing premise for the new derivations. The major weakness of the paper is the apparent error in Eq. (23): the amplitude-damped reduced density matrix misassigns the diagonal populations (the correct AD evolution gives |00> population (1+p^2)/2 and |11> population (1-p)^2/2, not the paper's (1-p+p^2)/2 for both). That is a correctness or arithmetic issue in the derivation, not a circularity: the formulas are still derived from stated inputs, but the inputs are applied incorrectly. Therefore, the circularity score is low, reflecting only the incidental prevalence of self-citations, none of which carry the derivation.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

No free parameters are fitted. The paper relies on standard channel theory, fidelity formulas, and a recent coherence measure. The central fragility is not circularity but a calculational error in the AD reduced state.

assumptions (6)

standard math Amplitude and phase damping are represented by Kraus operators given in Eqs. (18) and (31).
Standard quantum channel formalism (Nielsen and Chuang [19]); used throughout Secs. 4 and 5.
standard math Teleportation fidelity is F = (2 fmax + 1)/3, where fmax is the maximal singlet fraction over Bell states.
Horodecki et al. [30], Eq. (8); this is the standard two-qubit teleportation formula.
domain assumption Basis-independent coherence is defined by the Radhakrishnan-Ernakov-Byrnes entropy-based measure (Eq. 9).
The paper adopts this measure as the quantifier of coherence; it is not derived here.
standard math The three-tangle of the MS state is tau = sin^2(theta), and cos(theta) = sqrt(1-tau).
CKW formula for GHZ-class states (Eqs. 40-43).
domain assumption The teleportation channel is the reduced bipartite state obtained by tracing out the third qubit.
The protocol discards qubit C and uses rho_AB as the channel; this is a modeling choice (Sec. 6 makes it explicit).
standard math The MS state family is |MS(theta)> = (|000> + cos(theta)|110> + sin(theta)|111>)/sqrt(2).
Defined by Acin et al. [18], Eq. (1).

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Cite this review

Pith. "Pith review of Interplay between teleportation fidelity and basis-independent coherence in maximally sliced states under decoherence." pith.science (2026). https://pith.science/paper/HET6AQQ5

@misc{pith2026260803865,
  author       = {Pith},
  title        = {Pith review of: Interplay between teleportation fidelity and basis-independent coherence in maximally sliced states under decoherence},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HET6AQQ5}},
  note         = {Machine review of arXiv:2608.03865}
}

read the original abstract

The influence of environmental decoherence on quantum teleportation is investigated by considering the three-qubit Maximally Sliced (MS) state as the shared entangled resource. Using the Kraus operator formalism, analytical expressions are derived for the teleportation fidelity under amplitude damping and phase damping channels. The corresponding basis-independent coherence is obtained, establishing explicit analytical relations between coherence and teleportation fidelity under both decoherence mechanisms. The results are further expressed in terms of the Coffman-Kundu-Wootters (CKW) three-tangle, thereby connecting genuine tripartite entanglement with teleportation performance. The analysis reveals distinct effects of the two noise channels: amplitude damping introduces a state-dependent threshold for achieving quantum teleportation, whereas phase damping preserves the quantum advantage until complete dephasing. These results provide a unified analytical framework for understanding the interplay among multipartite entanglement, quantum coherence and teleportation in noisy three-qubit MS states.

Figures

Figures reproduced from arXiv: 2608.03865 by the authors.

**Figure 2.** Three-dimensional variation of the basis-independent coherence [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** Variation of the basis-independent coherence, [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

C. H. Bennett, G. Brassard, C. Cr´ epeau, R. Jozsa, A. Peres and W. K. Wootters,Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70(13), 1895, (1993)

work page 1993

[2] [2]

C. H. Bennett,Quantum information and computation, Phys. Today, 48(10), 24, (1995)

work page 1995

[3] [3]

Pirandola, J

S. Pirandola, J. Eisert, C. Weedbrook, A. Furusawa and S. L. Braunstein,Advances in quantum teleportation, Nat. Phot. 9(10), 641, (2015). 18

work page 2015

[4] [4]

J. Lee, H. Min and S. D. Oh,Multipartite entanglement for entanglement teleportation, Phys. Rev. A. 66(5), 052318, (2002)

work page 2002

[5] [5]

Kumar, S

A. Kumar, S. Adhikari, S. Banerjee and S. Roy,Optimal quantum communication using multiparticle partially entangled states, Phys. Rev. A. 87(2), 022307, (2013)

work page 2013

[6] [6]

Adhikari, A.S

S. Adhikari, A.S. Majumdar, S. Roy, B. Ghosh and N. Nayak,Teleportation via maximally and non-maximally entangled mixed states, Quant. Inf. and Comp., 5, 0398, (2010)

work page 2010

[7] [7]

Bhattacharjee, A

A. Bhattacharjee, A. Mandal and S. Roy,Teleportation of unknown qubit via Star-type tripartite states, 24(3), 65, (2025)

work page 2025

[8] [8]

Bhattacharjee, S

A. Bhattacharjee, S. Roy, M. M. Ali and B. Ghosh,Non-maximally entangled mixed states of X and non-X types as teleportation channels, Int. Jour. Theor. Phys. 63(5), 113, (2024)

work page 2024